1. Field of the Invention
The present invention concerns laser telemetry, in particular laser telemetry between two artificial bodies (for example, satellites in orbit or spacecraft) and/or natural bodies (for example, the Earth, the Moon or other planets) moving relative to each other with a transverse relative speed approaching or even exceeding a value in the order of one kilometer per second.
2. Description of the Prior Art
At present laser telemetry measures the time taken by a laser pulse to make the journey between a terrestrial laser station and a satellite (or the Moon) and converts the measured time into an "instantaneous" distance between a reference point of the laser station and the center of mass of the satellite (or a reference point, on the Moon) for example, correcting for various deterministic effects.
In the following description, the term laser telemetry is to be understood as referring to a measurement of the distance in either direction between satellites or, more generally, between natural or artificial heavenly bodies.
It should be borne in mind that all "laser" satellites currently in orbit around the Earth (e.g. the LAGEOS I and II, AJISAI, STARLETTE and STELLA satellites) were designed at a time when laser telemetry was somewhat inaccurate and the lasers employed were somewhat lacking in power (compared to what is available today). These satellites were therefore optimized to provide many small "cube-corner" retroreflectors capable of reflecting a detectable quantity of light to the transmitting station, whatever the orientation of the satellite. It was not very important that these retroreflectors were not all at exactly the same distance from the transmitting station, to within a few centimeters or within a few decimeters.
In recent years the situation has changed greatly, with the result that in present day laser telemetry stations the pulse duration of the laser can be as low as ten picoseconds (ps) (1 ps=10.sup.-12 seconds). The accuracy of measurement with a single echo from a laser having such small pulse duration is approaching one millimeter. However, the same cannot be said of the final measurement accuracy, in particular, because of the multiplicity of echos (one echo from each retroreflector visible from the laser transmitter at the time a pulse is transmitted) which space out the return pulses in time, there being no accurate way to associate each individual echo with the instantaneous distance between the center of mass and the satellite and the laser station.
The relative speed of the satellite and the laser station causes a speed aberration phenomenon which is corrected on existing satellites by making the angles between the mirror surfaces of the basic cube-corners slightly different from the nominal value of 90.degree..
Also, these cube-corners, which are usually solid, are deliberately made small (3 to 4 cm in diameter), for two reasons:
(1) because of the small corner angle defects, the diffraction pattern of the light wave that they reflect is a sort of continuous ring whose radius and width correspond to the values necessary for adequate compensation of speed aberration, rather than six distinct and separate lobes, and PA1 (2) because the cube-corners are small, the temperature gradients that occur within the glass from which they are made remains small, and consequently cause little degradation of the resulting diffraction pattern. PA1 return to the transmitting station receiver of a sufficient quantity of energy, adequate correction of speed aberration, and minimal "signature" (it is accepted that it is not essential for the retroreflection efficiency of the satellite to remain constant during movement of the satellite, which may not be known accurately); PA1 elimination of any influence which could widen the pulses reflected by the satellite; PA1 regardless of the geometry with which the light pulses impinge on the satellite, virtually no uncertainty (ideal accuracy is 1 mm or better) in determining the distance between a reference point of the laser station and the center of mass of the satellite from the measured distances to the retroreflectors. PA1 the shape of each surface is at least approximately that of a portion of a cone having an axis coincident with the associated edge, the generatrices of this portion of cone having a non-null average generatrix slope relative to a plane perpendicular to the axis of the cone portion, the average slope of the surface for all the generatrices being also non-null relative to the plane, PA1 the three surfaces have their respective concave side facing in the same direction relative to all of the three surfaces, PA1 the local slope along any generatrix of each surface is constant to within 20%, PA1 the average slope of each generatrix of each surface is within 30% of the average .alpha..sub.0 of the average slopes of the three surfaces, PA1 the average .alpha..sub.0 of the average slopes of the surfaces at least approximately satisfies the equation: EQU 0.2.delta./k PA1 at least one surface is formed by at least two triangular plane facets contiguous at a break line, the edges of each facet having, relative to the plane perpendicular to the axis of the surface, substantially equal slopes, PA1 each surface is made up of substantially identical facets, and preferably each surface is made up of two identical facets, and the three surfaces are identical PA1 the surface includes at least two successions of parallel steps separated by a transition whose height parallel to the axis of the surface corresponds to a phase step equal to a multiple of 2.pi. at least equal to one, PA1 the local slope of the generatrices of at least one of the surfaces varies with the distance from the apex, PA1 the local slope varies monotonously, and PA1 the slope of the generatrices of a surface varies circumferentially between the edges flanking the surface, preferably, PA1 the volume of the retroreflector is empty and the value of the coefficient k is 1, or alternatively PA1 the volume of the retroreflector is constituted by a homogeneous material of refractive index n and the value of the coefficient k is given by the equation: ##EQU1## where i.sub.0 is at least approximately 30.degree..
By choosing a small size, for the reasons explained above, reflectors are obtained whose efficiency (expressed as a fraction of the incident energy reflected to the transmitter) is low. Given the mean energy of the pulses transmitted by laser telemetry stations of 10 to 15 years ago, it was necessary to equip satellites with a large number of reflectors so that a sufficient quantity of light could be returned to the receiving telescope. Accordingly, all these satellites currently in orbit use the same principles and employ many cube-corners (from 60 to more than 2,000) with the result that their optical efficiency is virtually independent of their orientation relative to the transmitting station. The inevitable consequence of the above is a spreading in time of the reflected pulse (characterized by a "signature").
Even with highly sophisticated laser telemetry tools, this spreading effect makes it virtually impossible to determine the distance of satellites with an absolute accuracy better than one centimeter using a single transmitted pulse.
Against this background, the following requirements have to be met, if possible:
In the context of the requirements of geodesy as mentioned above, European Patent A-0 506 517 and French patent application 92 05989 of 18 May 1992 propose to mount a small number of large retroreflectors on a common structure to constitute a geodesy microsatellite enabling existing and future stations to achieve an accuracy in the order of one millimeter for measuring large distances.
The use of large hollow cube-corner retroreflectors (CCR) rather than the solid variety used on existing satellites should result in an adequate energy balance for the satellite plus CCR system. Given the energy and the duration of the pulses transmitted by modern laser telemetry stations, assuming orbits for this type of satellite between 300 km and 6,000 km above the Earth, and allowing for the angular spreading of the energy retroreflected by the CCR and the typical size of the receiving telescope of a station of this kind (i.e. an iris diameter in the order of 50 cm), it can be shown that a single retroreflector with an entry diameter typically between 10 cm and 20 cm can satisfy the energy balance requirements of the system.
It is accepted that the duration (half-amplitude width) of the laser pulses transmitted can typically be between 10 ps and 50 ps and that, strictly speaking, a single photon detected is sufficient to identify a CCR and to determine its distance (as is currently the case in laser telemetry between the Earth and the Moon). The uncertainty of any such measurement depends on the energy of the pulses detected; to a first approximation, it varies in inverse proportion to the square root of the number of photons detected. For example, if a 50 ps pulse gives a measurement uncertainty of 1 mm for ten photons detected at the receiver, the same result would probably be achieved for a single photon in the case of a 15 ps pulse. Note that this type of reasoning, valid in the case of a single echo, cannot be applied to conventional laser satellites because of the multiplicity of return echos which introduces an ambiguity as to the relation between the distance measured to the reflectors (which is dependent on the photons detected) and the (required) distance to the center of mass of the satellite, the distance being in each case that from the laser transmitter/receiver.
As indicated in the previously mentioned Europen Patent 0 506 517, if post-processing of the distance measurements is applied, the accuracy of the corrected measurements can be much greater than their intrinsic individual accuracy.
It is possible to determine a retroreflector diameter sufficient to avoid the need for very severe tolerances for the optics of its mirror surfaces. The same energy balance (or mean number of photons detected per pulse transmitted) requirements can be met with a very small number of large hollow CCR, rather than a large number of small CCR. Note that, unlike the solid CCR currently used on conventional laser satellites, there is no practical upper limit as to the size of hollow CCR.
For example, the inventors know of a 50 cm diameter CCR for the Japanese Agency ADEOS satellite (R.I.S.).
The previously mentioned French patent application 92-05989 discloses a set of eight cube-corners having their apexes close together, producing single and unambiguous return echos.
In the case of hollow cube-corners having their apexes close together, only incident rays at a grazing angle to the mirror surface of one of the cube-corners (and consequently of no utility on return to the station) may be in the area of visibility of one or more adjacent CCR. As this is a rare case, it can be assumed that this configuration is characterized by non-overlapping of the field of view of the retroreflectors, i.e. a single detected echo.
The problem therefore arises: of correcting the speed aberration in the case of a single large retroreflector if it is necessary to avoid any constraints in terms of attitude control or more generally in terms of the relative orientation of the laser transmitter/receiver (T/R) and the CCR.
The invention is directed to solving this problem in the context as already explained.
It is obvious that the most general solution for correcting the speed aberration in the case of a non-stabilized satellite is to have a diffraction pattern at infinity of each of the retroreflectors which is in the form of a uniform ring bordered by limited curves corresponding to angular distances equal to the extreme values of the speed aberration to be corrected (for example, typically between six seconds and ten seconds of arc for a satellite in orbit 800 km above the Earth).
French patent application 92-05989 proposes a solution with only two diffraction lobes, but this is feasible only if the relative orientation of the T/R and the CCR is known in advance and remains substantially constant.
In the general case where this relative orientation varies in time or is not known accurately, it would seem necessary to retain an annular shape for the diffraction pattern; as already explained, this cannot be done in combination with a high received energy flux (relative to the transmitted flux) for large distances between the T/R and the CCR.
To achieve this the invention proposes to impart to the wave surface after reflection a shape as close as possible to a cone. To achieve this deformation of the reflected light wave the invention proposes the use of a CCR whose mirror surfaces are at least approximately slightly conical, either continuously or discontinuously (stepped).